`lim_(x->oo)((x+2)/(x-1))^(x-3)`

Evaluate the limit: lim_(x rarr oo)((x+2)/(x+1))^(x+3)

Let f be a biquadratic function of x given by f(x) = Ax^4+Bx^3+Cx^2+Dx+E,where A,B,C,D,E in Rand 4!=0. If lim_(x->oo)(f(-x)/(2x^3))^(1/x)=e^-3, then

(lim_(xto oo) ((x+3)/(x+1))^(x+1) is equal to

lim_(x rarr oo)(x)/(x+1)

lim_(x rarr oo)((x-3)/(x+2))^(x) is equal to

lim_(x rarr oo)(1+(3)/(x))^(x)

lim_ (x rarr oo) ((x + 2) / (x-1)) ^ (x-3)

lim_(xto oo)(x/(1+x))^(x) is

lim_(x rarr oo)((x)/(1+x))^((x)/(2))=

lim_(x rarr oo)(x-1)/(x)